Matthew,
You may want to do LOTS of research by talking to people experienced at taking broken manifold studs out of heads in order to get as many hints and gotcha's warnings as possible before you start the process. It is frequently really tough to 1) drill the hole in the stud without accidently slipping and drilling into the head and 2) keeping the easy out from breaking. Broken easy outs generally don't come out easily, if at all. There is a better product than easy outs, I forget the name but Sears may carry them now. Remember that if the stud "wanted" to be removed, it wouldn't have broken when you tried to get it out.
A couple of possible hints (I'm not an expert but I've removed a few broken studs over the years):
Use lots of Liquid Wrench first . . . and let it soak before attempting to remove the stud. If you can safely do so, vibration (i.e. tapping it with a hammer/punch) can help Liquid Wrench do its thing. WD 40 may work as well as Liquid Wrench . . . I've never tried it since I always have LW on hand.
If the head is aluminum, try heating it with something like a propane torch (don't ignite the Liquid Wrench

) Aluminum will expand more than the steel stud and may make the hole bigger so it has less "grip" on the stud.
If there is a "stub" of the stud available to grip with Vise Grips, try using them first. Certainly don't cut off a centimeter (almost half an inch) of stud first. Try the vise grip approach first.
If the stub isn't long enough to grab, it may be long enough that you can use your dremel tool to cut a screw driver slot.
If you do drill, be sure to centerpunch the stud first and start with a small pilot bit first. Scott's idea of a left hand drill bit sounds good to me. I didn't know they exist.
Finally, if the head is off the car (or will be), take it to a Pro like Dennis Shaw. Then watch the Pro if possible so you learn.
Worst case (hopefully) will be having to drill out the stud and then tapping and helicoiling the hole. This is another "learning experience" opportunity.